Kinetic Theory

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(d) When number of molecules breaks then number of moles would become double.

P $\propto nT$ where n is the number of moles and T is temperature of ideal gas

As gases breaks number of moles becomes twcice of initial so n₂ =2n₁

$\frac{P_2}{P_1}=\frac{n_2{T}_2}{n_1{T}_1}=\frac{2n_1\left(3000\right)}{n_1\left(300\right)}$ = 20

p₂=20p₁

so 20 tim

This is a multiple choice answer as classified in NCERT Exemplar

(a) Pressure is inversely proportional to slope

So $\frac{p_1}{}$$\frac{p_{}}{}$$\frac{2_{}}{}=\frac{m_2}{m_1}\mathrm{<1}$

So p₁ > p₂

This is a multiple choice answer as classified in NCERT Exemplar

(c) The pressure inside the gas will be 

P= p_a+Mg/A

A= area of piston

P_a= atmospheric pressure

Mg = weight of piston

When temperature is increases

pV=nRT so volume increases at constant pressure.

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(b) Boyle's law is applicable when temperature is constant

PV=nRT=constant

PV= constant

So pressure is inversely proportional to volume.

So process is called isothermal process.

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(d) In an ideal gas when a molecules collides elastically with a wall, the momentum transferred to each molecule will be twice the magnitude of its normal momentum. For the face EFGH, it transfer only half of that.

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(b) As the motion of the vessel as a whole does not affect the relative motion of the gas molecules with respect to the walls of the vessel, hence pressure of the gas inside the vessel, as conserved by us, on the ground remains the sam

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According to kinetic interpretation of temperature, absolute temperature of a given sample of a gas is proportional to total translational kinetic energy of its molecule.

Hence any change in absolute temperature of a gas will contrib

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Volume occupied by 1 mole = 1mole of the gas at NTP= 22400mL=22400cc

So number of molecules in 1cc of hydrogen= $\frac{6.023\times {10}^{23}}{22400}=2.688\times {10}^{19}$

H₂ is a diatomic gas, having a total of 5 degrees of freedom

So total degrees possesed by all the molecules

= 5 $\times 2.688$ $\times {10}^{19}=1.344\times {10}^{20}$

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Number of helium = 5

T=7^oC=7+273=280K

(a) hence number of atoms = number of moles $*$ Avogadro's number

= $5*6.023*{10}^{23}=30.015*{10}^{23}=3*{10}^{24}$ atoms

(b) now average kinetic energy per molecule = 3/2 K_BT

= total internal energy

= $\frac{3}{2}{K}_{b}T*$ number of atoms

= $\frac{3}{2}*1.38*{10}^{-23}*280*3*{10}^{24}=1.74*{10}^{4}J$

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When air is pumped, more molecules are pumped and boyle's law is staed for situation where number of molecules remains constant . in this case as the number of air molecules keep increases, hence mass change. Boyle's law is only app